Problem: Solve for $x$ and $y$ using elimination. ${5x+2y = 44}$ ${-6x-5y = -71}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $6$ and the bottom equation by $5$ ${30x+12y = 264}$ $-30x-25y = -355$ Add the top and bottom equations together. $-13y = -91$ $\dfrac{-13y}{{-13}} = \dfrac{-91}{{-13}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {5x+2y = 44}\thinspace$ to find $x$ ${5x + 2}{(7)}{= 44}$ $5x+14 = 44$ $5x+14{-14} = 44{-14}$ $5x = 30$ $\dfrac{5x}{{5}} = \dfrac{30}{{5}}$ ${x = 6}$ You can also plug ${y = 7}$ into $\thinspace {-6x-5y = -71}\thinspace$ and get the same answer for $x$ : ${-6x - 5}{(7)}{= -71}$ ${x = 6}$